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README.md

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# AMG
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[![Build Status](https://travis-ci.org/ranjanan/AMG.jl.svg?branch=master)](https://travis-ci.org/ranjanan/AMG.jl)
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[![Coverage Status](https://coveralls.io/repos/ranjanan/AMG.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/ranjanan/AMG.jl?branch=master)
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[![codecov.io](http://codecov.io/github/ranjanan/AMG.jl/coverage.svg?branch=master)](http://codecov.io/github/ranjanan/AMG.jl?branch=master)
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This package lets you solve sparse linear systems using Algebraic Multigrid (AMG). This works especially well for symmetric positive definite matrices.
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## Usage
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```julia
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using AMG
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A = poisson(1000) # Creates a sample symmetric positive definite sparse matrix
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ml = ruge_stuben(A) # Construct a Ruge-Stuben solver
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# Multilevel Solver
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# -----------------
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# Operator Complexity: 1.9859906604402935
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# Grid Complexity: 1.99
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# No. of Levels: 8
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# Coarse Solver: AMG.Pinv()
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# Level Unknowns NonZeros
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# ----- -------- --------
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# 1 1000 2998 [50.35%]
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# 2 500 1498 [25.16%]
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# 3 250 748 [12.56%]
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# 4 125 373 [ 6.26%]
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# 5 62 184 [ 3.09%]
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# 6 31 91 [ 1.53%]
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# 7 15 43 [ 0.72%]
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# 8 7 19 [ 0.32%]
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solve(ml, A * ones(1000)) # should return ones(1000)
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```
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## Roadmap
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This package currently supports:
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1. Ruge-Stuben Solver
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2. Classical Strength of Connection
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3. Ruge-Stuben C/F splitting
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4. Gauss-Siedel smoothers
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5. V cycle multigrid
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In the future, this package will support
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1. SmoothedAggregation Solver
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2. Standard Strength of Conneciton
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3. Other splitting methods (like CLJP)
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4. SOR, Jacobi smoothers
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5. W, F, AMLI cycles

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